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On logarithmic Hölder continuity of mappings on the boundary. (English) Zbl 1489.30034

It is well known that quasiconformal mappings are locally Holder continuous. There are many generalizations of this fact to more general classes of mappings. Often for these more general mappings the Hölder continuity fails, but logarithmic Hölder continuity holds. This paper studies mappings satisfying the inverse Poletsky inequality where the corresponding majorant is integrable. In a previous paper the author (together with co-authors) proved that these mappings are locally logarithmic Hölder continuous and admit continuous extension to the boundary. In the current paper the author shows that these mappings are also locally logarithmic Hölder continuous in the closure of the domain (of the mapping).

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
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References:

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